Per Delsing Fig. 1

Coherent oscillations in a Single CooperCoherent oscillations in a Single Cooper--pair Boxpair Box

1.1. IntroductionIntroduction

2.2. Coulomb StaircaseCoulomb Staircase

3.3. SpectroscopySpectroscopy

4.4. Coherent oscillations

CHALMERS:Experiment:Tim DutyDavid GunarssonKevin Bladh

Theory:G. Johansson =>KarlsruheA. KäckG. Wendin

YALE:Rob SchoelkopfKonrad Lehnert =>Bolder

Coherent oscillations

Per Delsing Fig. 2

A Single CooperA Single Cooper--pair Box pair Box QubitQubitIntegrated with an RFIntegrated with an RF--SET ReadSET Read--out systemout system

RF-SET

V

singleCooper-pairbox

∆ >> EC >> EJ(B) >> T2.5K 1K 0.5-0.05K 20mK

Bouchiat et al. Physica Scripta (99)Makhlin et al. Rev. Mod. Phys. (01)Aassime, PD et al., PRL (01)

Per Delsing Fig. 3

The Single CooperThe Single Cooper--pair box (SCB)pair box (SCB)

Vg Q=n2e

C1

C2

H =Q2

2CΣ

− EJ cosθ

c.f. Hamiltonian for Bloch electronsp2

2m+U (x)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

E /

EC EJ

n g

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

<n>

ng

Bouchiat et al., Physica Scripta (98)Nakamura et al., Nature (99)Makhlin et al., Nature (00)

Per Delsing Fig. 4

The RadioThe Radio--FrequencyFrequencySingle Electron TransistorSingle Electron Transistor

3210-1

Qgate (e)

Average conductance Reflected power

Vg CSET

CQB

CCCg

SingleCooper-pair

Box

L

C

SingleElectron

Transistor

DirectionalCoupler

Mixer

SET-biasPulse line50 GHz

Tank circuit

ColdAmplifier

WarmAmplifier

~RF-source450 MHz Output

RFLO

Bias-Tee

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0 5 10 15 20 25 30 35 40

Cha

rge

(e)

Time(µs)

ĘQ=0.1eBw=1MHz

Very high speed:137 MHzR.Schoelkopf, PD et al. Science (98)

Very high sensitivity:3.2 µe/√HzA.Aassime, PD et al.APL (01)

Per Delsing Fig. 5

SET IVSET IV--characteristics andcharacteristics andConductance vs. Conductance vs. VVbb and Vand Vgg

B=0.0 T B=0.4 T

Operation pointdouble JQP

-5

0

5

10

15

20

Vg

V bi

as

-0.02 0 0.02

-1

-0.5

0

0.5

1-5

0

5

10

15

20

-0.02 0 0.02

-1

-0.5

0

0.5

1

V bi

as

Vg

-20

-15

-10

-5

0

5

10

15

20

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

I (nA

)

V (mV)

RSET=44.1k½C· =370 aFCgÅ20aF

Per Delsing Fig. 6

The Sample holderThe Sample holderFabricated in oxygen free high conductivitycopper and gold plated

Inductance can be changed by changing the distance to the ground plane with a tuning screw

Inductor can be made Superconducting tominimize losses

Tank circuit : L≈400nH, Cpad≈300fF

0

5

10

15

20

25

30

35

260 280 300 320 340 360 380 400 420

P(1µA)-P(0,no Yoko)

Shot

noi

se p

ower

(nW

)

Frequency (MHz)

Q≈17.4fc=330.8 MHz

fBW=9.5MHz

Shot noise from the SET, I=1µAShot noise from the SET, I=1µA

Per Delsing Fig. 7

Improving sensitivity by adding a SQUID amplifierImproving sensitivity by adding a SQUID amplifier

Washer

Coilin

Coilend

CE

Cold HEMT amplifiers has TN≈ 2.5 K

SQUID amplifier has TN≈ 50 mKCollaboration with BerkeleyM. Mück, J.B. Kycia, and J. ClarkeAppl. Phys. Lett., 78, 967 (2001)

A transmission RF-SET would then be betterT. Fujisawa and Y. HirayamaAppl. Phys. Lett., 77, 543 (2000)

CSETCC

L

C

50 GHzQubit

manipulation

Tank circuit

Bias-Tee

HEMTAmplifier

SQUIDAmplifier

Mixer

WarmAmplifier

X~ Output

RF

LO

L

SET-bias

SingleCooper-pair

Box

C QB

C g

SingleElectron

Transistor

RF-source450 MHz

Per Delsing 8

QubitQubit measurementsmeasurements

Per Delsing Fig. 9

C· SETC· QB

CC

23aF13aF

EcQ=1.67K, 560aF 620aF, Ec=1.51K

10aF

Coupling = 1.9%

Circuit parametersCircuit parameters

RSET≈45kΩECSET≈1.51KECBOX≈1.65KEJ≈0.6KBox to SET coupling=1.9%B-field parallel to substrate fcarrier=450 MHzRF-amplitude≈-100dBmStaircase sweep frequency =141Hz

Per Delsing Fig. 10

The Coulomb blockade staircase, normal stateThe Coulomb blockade staircase, normal state

0.0

1.0

2.0

3.0

4.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

ExperimentTheory

Ave

rage

box

cha

rge

[e]

CgVg [e]

Per Delsing Fig. 11

The Coulomb blockade staircase, comparingThe Coulomb blockade staircase, comparingthe normal and thethe normal and the superconductingsuperconducting statestate

0

1

2

3

4

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Normal stateSuperconducting state: Sample 1Superconducting state: Sample 2

Box

Cha

rge

[e]

CgVg [e]

Per Delsing Fig. 12

What would you expect in theWhat would you expect in the superconductingsuperconducting statestate

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.5 1 1.5 2

E/E

C

ng

² ~

∆~≈∆0-kBT ln(N)

∆0≈2.4K for Al

∆~=(L-S)/(L+S)

Lafarge et al. Nature (93)

Per Delsing 13

Long Step versus Short StepLong Step versus Short Step

Per Delsing Fig. 14

Magnetic field dependence of the short stepMagnetic field dependence of the short step

0.0

2.0

4.0

6.0

8.0

10.0

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0

B= 667.5 mTB= 623.0 mTB= 578.5 mTB= 534.0 mTB= 489.5 mTB= 445.0 mTB= 400.5 mTB= 356.0 mTB= 311.5 mTB= 267.0 mTB= 222.5 mTB= 178.0 mTB= 133.5 mTB= 89.0 mTB= 44.5 mT

aver

age

char

ge [e

]

CgVg [e]

Per Delsing Fig. 15

The odd even energy differenceThe odd even energy difference

0.0

0.5

1.0

1.5

2.0

2.5

0.0 0.2 0.4 0.6 0.8 1.0

Ę~ sample 1

fit values

Ę til

de [K

]

B|| [T]

2e regionsample 2

≈∆0-kBT ln(N)

∆0≈2.4K for Al

=(L-S)/(L+S)

Lafarge et al. Nature (93)

˜ ∆

˜ ∆

Extracting ˜ ∆ (B) :

Per Delsing 16

SpectroscopySpectroscopy

Per Delsing Fig. 17

Microwave irradiation of the CooperMicrowave irradiation of the Cooper--pair boxpair boxFrequency dependenceFrequency dependence

2.0

3.0

4.0

2.4 3.0 3.6

50 GHz42 GHz34 GHz30 GHz

Ave

rage

cha

rge

[e]

CgVg [e]

Limited frequency range

25-50 GHz

Two photon peaks

=> > 50 GHz

(Averaging causes broad peaks)

Per Delsing Fig. 18

Energy levels extracted from spectroscopyEnergy levels extracted from spectroscopy

0

10

20

30

40

50

60

70

0.0 0.1 0.2 0.3 0.4 0.5

EJ = maxEJ Å0, single photon peaksEJ Å0, two photon peaks

f [G

Hz]

Æn

EC=1.67 KEJ=0.6 K

Per Delsing Fig. 19

Spectroscopy Spectroscopy BB--field dependencefield dependence

Modulation of Ej with B||Irradiation by 50 GHz µ-waves1

3 0.8

0.62

<n>

0.4

0.21

0 0.9 1 1.10 0.5 1.0 1.5 2.0B|| [Telsa]Cg Vg

Per Delsing 20

Coherent oscillationsCoherent oscillations

Per Delsing Fig. 21

Nakamura, Nakamura, PashkinPashkin and Tsai (1999and Tsai (1999)

Nakamura et al., Nature (99)

Per Delsing Fig. 22

Continuous measurement with Continuous measurement with TTrr=59ns, amplitude 1e pulse train=59ns, amplitude 1e pulse train

0 1 2 3 40

1

2

3

4

5pulse train offpulse train on

<n>

CgVg [e]

Tr

Per Delsing Fig. 23

Coherent OscillationsCoherent Oscillations

][ pst∆gate charge n

g

0 0.2 0.4 0.6 0.8 1 1.2100

200

300

400

500

∆t [p

s]

0 0.2 0.4 0.6 0.8 1 1.2500

1000

1500

0 0.2 0.4 0.6 0.8 1 1.21500

2000

2500

0

0.2

0.4

0.6

0

0.2

0.4

0

0.2

0.4 Period=70 ps agrees well with Ej

Color represents difference between pulsed staircase and ”unpulsed” staircase

Per Delsing Fig. 24

Signal versus pulse durationSignal versus pulse duration

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0 0.5 1 1.5 2 2.5

<n>

[e]

Ęt [ns]

Per Delsing Fig. 25

Possible sources of Possible sources of decoherencedecoherence

• Continuous measurement of course decoheres the system, pulsed measurements should improve the situation.

• Non-equilibrium quasi particles are obviously present in the system.

• Non-perfect dc pulses: the pulse is not perfectly square and thus the system is not exactly at the degeneracy point during the evolution. Therefore background charge noise couples stronger to the system

Per Delsing Fig. 26

SummarySummary

•RF-SET optimized, ∂Q=3.2 µe/√Hz achieved

•Fabrication of integrated Qubit and RF-SET

•Characterization of Cooper-pair box

– Demonstrated continuous (and pulsed) read-out of box charge.

– Observation of microwave induced transitions between |0> and |2>

– Determination of EC and EJ from spectroscopy.

– Coherent Oscillations observed (reproduced Nakamura’s results with RF-SET read-out).